The Omicron variant of SARS-CoV-2 infected many vaccinated and convalescent individuals^{, –}. Despite the reduced protection from infection, individuals who received three doses of an mRNA vaccine were highly protected from more serious consequences of infection. Here we examine the memory B cell repertoire in a longitudinal cohort of individuals receiving three mRNA vaccine doses^,. We find that the third dose is accompanied by an increase in, and evolution of, receptor-binding domain (RBD)-specific memory B cells. The increase is due to expansion of memory B cell clones that were present after the second dose as well as the emergence of new clones. The antibodies encoded by these cells showed significantly increased potency and breadth when compared with antibodies obtained after the second dose. Notably, the increase in potency was especially evident among newly developing clones of memory cells, which differed from persisting clones in targeting more conserved regions of the RBD. Overall, more than 50% of the analysed neutralizing antibodies in the memory compartment after the third mRNA vaccine dose neutralized the Omicron variant. Thus, individuals receiving three doses of an mRNA vaccine have a diverse memory B cell repertoire that can respond rapidly and produce antibodies capable of clearing even diversified variants such as Omicron. These data help to explain why a third dose of a vaccine that was not specifically designed to protect against variants is effective against variant-induced serious disease.